I think the only way to document your family is to create your own tree. If you are thinking of the Stiernstam name in the list of Swedish nobility I linked to, it was extinguished with the death of Gustaf's brother Carl Wilhelm Stiernstam 12 Dec 1929. The nobility runs only in the male line, I understand.
There will have been an estate inventory (in Swedish : "bouppteckning") made after Gustaf's death and the Landsarkivet i Göteborg may be able to help you find it. Try writng to
landsarkivet.gla[at]riksarkivet.se and let the [at] become a @.